These findings emphasize the high importance of choosing an appropriate base distribution for NFs. We therefore propose to generalize the isotropic Gaussian to a much broader class of distributions—the class of copula distributions. Copulae are a well-known concept in statistical theory and are being used to model complex distributions in finance, actuarial science, and extreme-value theory [1]}, [2]}, [3]}. Broadly speaking, a copula is some function that couples marginal distributions to a multivariate joint distribution. Hence, copulae allow for flexible multivariate modeling with marginals stemming from a huge range of suitable classes.
This allows for example to formulate NF base distributions that combine heavy-tailed marginals—as proposed by [4]}, [5]}, [6]}—with light-tailed marginals.
This paper presents a novel framework for choosing the base distribution of NFs building on the well-studied theory of copulae. A first empirical investigation demonstrates the benefits brought by this approach.
Our experimental analysis on toy data reveals that using even the most simple copula model—the Independence Copula—we are able to outperform the vanilla NF approach, which uses an isotropic Gaussian base distribution.
The resulting NF converges faster, is more robust, and achieves an overall better test performance. In addition, we show that the learned transformation has a better-behaved functional form in the sense of a more stable local Lipschitz continuity.
